Fused-deposition modeling is a technique for building a three-dimensional object from a mathematical model of the object. In general, the object is built by feeding a thermoplastic filament into a heated extrusion head. The heated extrusion head melts and deposits the molten thermoplastic material as a series of beads. Each bead is roughly spherical or cylindrical in shape—and is much like the toothpaste that is squeezed from a tube—but much smaller than a grain of rice. Typically, a bead is between 0.001th to 0.010th of an inch thick. When a bead is deposited, it is just slightly above its melting point. After it is deposited, the bead quickly solidifies and fuses with the beads that are next to and below it.
Perhaps the greatest advantage of fused-deposition modeling is that it can build an object of any shape. To accomplish this, however, there are constraints on the sequence in which the beads can be deposited. First, each bead must be supported. In other words, a bead cannot be deposited on air. Therefore, each bead must be deposited on:                (i) a platform that is not part of the object, or        (ii) one or more previously-deposited beads that will be part of the object, or        (iii) a temporary scaffold of support material that is not part of the object, or        (iv) any combination of i, ii, and iii.Second, when a three-dimensional surface is sealed with beads, it is no longer possible to deposit a bead inside of that surface. This is analogous to the situation in which once you close a box, you can't put anything into the box.        
There is a general methodology that is used in fused-deposition modeling that satisfies these constraints and enables the building of an object of any shape. The three-dimensional model of the object is modeled as thousands of thin layers in the X-Y plane. Each layer is modeled as thousands of beads and voids. The object is then built, one bead at a time, one layer at a time, only in the +Z direction.
There are, however, costs and disadvantages associated with traditional fused-deposition modeling.